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  • 1.
    Johansson, Anders
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Öberg, Anders
    Square summability of variations of g-functions and uniqueness of g-measures2003In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 10, no 5, p. 587-601Article in journal (Refereed)
    Abstract [en]

    We prove uniqueness of $g$-measures for $g$-functions satisfying quadratic summability of variations. Our result is in contrast to the situation of, \eg, the one-dimensional Ising model with long-range interactions, since $\ell_1$-summability of variations is required for general potentials. We illustrate this difference with some examples. To prove our main result we use a product martingale argument. We also give conditions for uniqueness of general $G$-measures, \ie, the case for general potentials, based on our investigation of the probabilistic case involving $g$-functions.

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